Three Dimensional Geometry JEE Main PYQs PDF, 2020–2026

Three Dimensional Geometry has 297 questions in JEE Main papers from 2020 to 2026, about 42 per year across all shifts. All 297 are in the free PDF, with an answer key. The most asked topic is Equation of Line in 3D (83 questions), followed by Skew Lines and Shortest Distance (70) and Equation of Plane (60).

Asked in JEE Main: 2972020–2026, all shifts
In this free PDF: 297all of them, with answers
Asked in 2026: 32Latest paper: 2026 Apr S2
Most asked topic: Equation of Line in 3D83 Qs · 28% of the chapter
Difficulty mix: 2% easy · 91% medium · 7% hardof the questions in the PDF

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Source: official NTA JEE Main papers · Updated 17 Oct 2026

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23 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Three Dimensional Geometry had about 1.8 questions per shift in recent JEE Main papers (2024–26). It's one of the most asked Mathematics chapters. Most asked topic: Equation of Line in 3D. About 32 questions in the 2026 papers. (Some topics were cut in 2024; see what changed.)

It came up in every 2024–26 shift in our bank. Question types in 2020–2026: about 211 MCQs and about 86 numerical.

How many questions from Three Dimensional Geometry in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	32	1.7	27	5
2025	34	1.8	31	3
2024	40	2.0	25	15
2023	71	3.0	48	23
2022	47	2.0	31	16
2021	54	2.1	35	19
2020	19	1.2	14	5
2020–2026	297	2.0	211	86

Most asked Three Dimensional Geometry topics, 2020–2026

Topic	Questions
Equation of Line in 3D	83
Skew Lines and Shortest Distance	70
Equation of Plane	60
Distance and Angle in 3D	45
Distance of Point from Plane	20

Every topic, year by year, is in the topic-wise table further down.

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 17 Oct 2026.

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Two free sheets, made from the past JEE Main questions on this chapter.

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Three Dimensional Geometry questions per year

Year	Asked	In PDF
2026	32	32
2025	34	34
2024	40	40
2023	71	71
2022	47	47
2021	54	54
2020	19	19

Topic-wise weightage by year

How many Three Dimensional Geometry questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Equation of Line in 3D	83	28%	23	20	15	7	4	10	4
Skew Lines and Shortest Distance	70	23%	5	10	19	18	6	8	4
Equation of Plane	60	20%	·	·	·	20	12	21	7
Distance and Angle in 3D	45	15%	3	3	3	15	10	8	3
Distance of Point from Plane	20	7%	·	·	·	7	8	4	1
Direction Cosines and Ratios	14	5%	1	1	3	3	4	2	·
Angle Between Planes	5	2%	·	·	·	1	3	1	·
All topics	297	100%	32	34	40	71	47	54	19

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 32 JEE Main 2026 Three Dimensional Geometry questions in the free PDF, latest shift first.

JEE Main 2026 · 8 Apr · Shift 2 · Equation of Line in 3D

Let a line $L_{1}$ pass through the origin and be perpendicular to the lines

${\mathrm{L}}_{2}:\overrightarrow{{\mathrm{r}}}=(3+{\mathrm{t}}){\hat{i}}+(2{\mathrm{t}}-1){\hat{j}}+(2{\mathrm{t}}+4){\hat{k}}$ and

${\mathrm{L}}_{3}:\overrightarrow{{\mathrm{r}}}=(3+2{\ \mathrm{s}}){\hat{i}}+(3+2{\ \mathrm{s}}){\hat{j}}+(2+{\mathrm{s}}){\hat{k}},{\mathrm{t}},{\mathrm{s}}\in {\mathbf{R}}$ .

If $(a,b,c),a\in {\mathbf{Z}}$ , is the point on ${\mathrm{L}}_{3}$ at a distance of $\sqrt{17}$ from the point of intersection of ${\mathrm{L}}_{1}$ and ${\mathrm{L}}_{2}$ , then $({\mathrm{a}}+{\mathrm{b}}+{\mathrm{c}})^{2}$ is equal to $\_\_\_\_$ .
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JEE Main 2026 · 8 Apr · Shift 2 · Skew Lines and Shortest Distance

Let the foot of perpendicular from the point $(\lambda,2,3)$ on the line $\frac{x-4}{1}=\frac{y-9}{2}=\frac{z-5}{1}$ be the point ( $1,\mu,2$ ). Then the distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}$ and $\frac{x-\lambda}{2}=\frac{y-\mu}{3}=\frac{z+5}{6}$ is equal to :

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JEE Main 2026 · 6 Apr · Shift 1 · Equation of Line in 3D

Let the image of the point ${\mathrm{P}}(1,6,a)$ in the line ${\mathrm{L}}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b},b>0$ , be $\left(\frac{a}{3},0,a+c\right)$ . If ${\mathrm{S}}(\alpha,\beta,\gamma),\alpha>0$ , is the point on L such that the distance of S from the foot of perpendicular from the point P on L is $2\sqrt{14}$ , then $\alpha+\beta+\gamma$ is equal to:
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JEE Main 2026 · 6 Apr · Shift 2 · Equation of Line in 3D

Let the image of the point ${\mathrm{P}}(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point ${\mathrm{Q}}\left(0,\frac{-1}{2},0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the point S . Then the square of the area of the parallelogram PQRS is $\_\_\_\_$ .
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JEE Main 2026 · 6 Apr · Shift 2 · Skew Lines and Shortest Distance

The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is:
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JEE Main 2026 · 6 Apr · Shift 1 · Distance and Angle in 3D

Let a line L be perpendicular to both the lines ${\mathrm{L}}_{1}:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and ${\mathrm{L}}_{2}:\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$ .

If $\theta$ is the acute angle between the lines L and ${\mathrm{L}}_{3}:\frac{x-\frac{8}{7}}{2}=\frac{y-\frac{4}{7}}{1}=\frac{z}{2}$ , then $\tan \theta$ is equal to:

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JEE Main 2026 · 5 Apr · Shift 1 · Equation of Line in 3D

The square of the distance of the point of intersection of the lines ${\vec{r}}=({\hat{i}}+{\hat{j}}-{\hat{k}})+\lambda(a{\hat{i}}-{\hat{j}}),a\neq 0$ and ${\vec{r}}=(4{\hat{i}}-{\hat{k}})+\mu(2{\hat{i}}+a{\hat{k}})$ from the origin is :
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JEE Main 2026 · 5 Apr · Shift 2 · Equation of Line in 3D

Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from $R(1,2,3)$ . If $(\alpha,\beta,\gamma)$ is the centroid of $\Delta PQR$ , then $\alpha+\beta+\gamma$ is equal to :
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JEE Main 2026 · 5 Apr · Shift 1 · Distance and Angle in 3D

The square of the distance of the point ${\mathrm{P}}(5,6,7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:
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JEE Main 2026 · 5 Apr · Shift 2 · Equation of Line in 3D

If the distance of the point $(a,2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is 4 , then the sum of all possible values of $a$ is equal to :
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JEE Main 2026 · 4 Apr · Shift 2 · Equation of Line in 3D

If $\left(2\alpha+1,\alpha^{2}-3\alpha,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line $\frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}$ , then the possible value(s) of $\alpha$ is (are)

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JEE Main 2026 · 4 Apr · Shift 1 · Equation of Line in 3D

The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line $\frac{x+5}{1}=\frac{y+5}{-1}=\frac{z}{2}$ is equal to:

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JEE Main 2026 · 4 Apr · Shift 2 · Skew Lines and Shortest Distance

The shortest distance between the lines

${\vec{r}}=\left(\frac{1}{3}{\widehat{{\mathrm{i}}}}+2{\widehat{{\mathrm{j}}}}+\frac{8}{3}{\widehat{{\mathrm{k}}}}\right)+\lambda(2{\widehat{{\mathrm{i}}}}-5{\widehat{{\mathrm{j}}}}+6{\widehat{{\mathrm{k}}}})$

and ${\vec{r}}=\left(-\frac{2}{3}{\widehat{{\mathrm{i}}}}-\frac{1}{3}{\widehat{{\mathrm{k}}}}\right)+\mu({\widehat{{\mathrm{j}}}}-{\widehat{{\mathrm{k}}}}),\lambda,\mu\in {\mathbb{R}}$ , is:

(A)
$\sqrt{5}$
(B)
3
(C)
$2\sqrt{3}$
(D)
$\sqrt{15}$

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Answer: (B)

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JEE Main 2026 · 23 Jan · Shift 1 · Direction Cosines and Ratios

Let the direction cosines of two lines satisfy the equations : $4l+m-n=0$ and $2mn+10nl+3lm=0$ .

Then the cosine of the acute angle between these lines is :

(A)
$\frac{10}{7\sqrt{38}}$
(B)
$\frac{10}{\sqrt{38}}$
(C)
$\frac{10}{3\sqrt{38}}$
(D)
$\frac{20}{3\sqrt{38}}$

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Answer: (C)

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JEE Main 2026 · 21 Jan · Shift 2 · Distance and Angle in 3D

Let the line L pass through the point $(-3,5,2)$ and make equal angles with the positive coordinate axes. If the distance of L from the point $(-2,r,1)$ is $\sqrt{\frac{14}{3}}$ , then the sum of all possible values of $r$ is :

(A)
16
(B)
12
(C)
6
(D)
10

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Answer: (D)

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JEE Main 2023 · 15 Apr · Shift 1 · Equation of Plane

Let the plane

P

contain the line

2 x+y-z-3=0=5 x-3 y+4 z+9

and be

parallel to the line

\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}

. Then the distance of the point

\mathrm{A}(8,-1,-19)

from the plane

\mathrm{P}

measured parallel to the line

\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}

is equal to ______________.

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Answer: 26

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JEE Main 2023 · 13 Apr · Shift 2 · Distance of Point from Plane

Let $\mathrm{N}$ be the foot of perpendicular from the point $\mathrm{P}(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$ . Then the distance of $N$ from the plane $2 x-2 y+z+5=0$ is :

(A)7
(B)6
(C)9
(D)8

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Answer: (A)

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JEE Main 2023 · 30 Jan · Shift 1 · Angle Between Planes

If $\lambda_{1} < \lambda_{2}$ are two values of $\lambda$ such that the angle between the planes $P_{1}: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_{2}: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$ , then the square of the length of perpendicular from the point $\left(38 \lambda_{1}, 10 \lambda_{2}, 2\right)$ to the plane $P_{1}$ is ______________.

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Answer: 315

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Frequently asked

How many questions come from Three Dimensional Geometry in JEE Main?

297 questions from 2020 to 2026, about 42 per year. In 2026 it had 32.

Which Three Dimensional Geometry topics are most important for JEE Main?

By past papers: Equation of Line in 3D (28%), Skew Lines and Shortest Distance (23%) and Equation of Plane (20%) of all Three Dimensional Geometry questions.

Is the Three Dimensional Geometry PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Three Dimensional Geometry online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020

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Answers follow NTA's final answer keys. Typing errors are possible, so check doubtful answers against the official key. Spotted a mistake? prepwiser.in/feedback · Terms: prepwiser.in/terms

Three Dimensional Geometry JEE Main PYQs PDF, 2020–2026

How often it's asked in JEE Main

How many questions from Three Dimensional Geometry in JEE Main, year by year

Most asked Three Dimensional Geometry topics, 2020–2026

Revise Three Dimensional Geometry before you practise

Send this chapter to your study group

Three Dimensional Geometry questions per year

Topic-wise weightage by year

Newest questions (2026)

Sample questions from recent papers

Practise these online, free, no login

Frequently asked

How many questions come from Three Dimensional Geometry in JEE Main?

Which Three Dimensional Geometry topics are most important for JEE Main?

Is the Three Dimensional Geometry PYQ PDF free?

More Mathematics chapters